Analysis and partial differential equations on manifolds, fractals and graphs / edited by Alexander Grigor'yan, Yuhua Sun.

Format:

Book

Contributor:

Grigori︠a︡n, A., editor.

Sun, Yuhua, editor.

Series:

Advances in analysis and geometry ; Volume 3.

Advances in Analysis and Geometry ; Volume 3

Language:

English

Subjects (All):

Differential equations, Partial.

Physical Description:

1 online resource (VIII, 518 p.)

Place of Publication:

Berlin ; Boston : De Gruyter, [2021]

Language Note:

In English.

Summary:

The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.

Contents:

Frontmatter

Contents

Preface

Part I: Fractals and graphs

Stability of heat kernel estimates and parabolic Harnack inequalities for general symmetric pure jump processes

The pointwise existence and properties of heat kernel

Resistance estimates and critical exponents of Dirichlet forms on fractals

A survey on unbounded Laplacians and intrinsic metrics on graphs

Energy measures for diffusions on fractals: a survey

Hyperbolic graphs induced by iterations and applications in fractals

Geometric implications of fast volume growth and capacity estimates

Parabolic index of an infinite graph and Ahlfors regular conformal dimension of a self-similar set

Metrics and uniform Harnack inequality on the Strichartz hexacarpet

Part II: Euclidean spaces and manifolds

Analysis on manifolds and volume growth

Geometric analysis on manifolds with ends

A matrix Harnack estimate for a Kolmogorov type equation

Entropy power concavity inequality on Riemannian manifolds and Ricci flow

Fractional differential operators and divergence equations

Interior gradient estimates for mean curvature type equations and related flows

An alternate induction argument in Simons’ proof of holonomy theorem

Higher integrability for nonlinear nonlocal equations with irregular kernel

On nonexistence results of porous medium type equations and differential inequalities on Riemannian manifolds

Index

Notes:

Description based on print version record.

ISBN:

3-11-070076-X

OCLC:

1232280064